1. Field of the Invention
The present invention relates to the field of petrophysical measurements on rock samples. More particularly, the invention relates to processes for characterizing the three-dimensional distribution of the absolute permeability of a heterogeneous sample from a rock.
2. Description of the Invention
There are different known approaches for characterizing a three-dimensional (3D) permeability map of a rock sample.
Identification of a 3D Map Based on “Manual” Identification
This approach uses a tracer test, that is a miscible test but without viscosity contrast, to obtain a permeability map. This technique is described in the following documents:                Dabbouk, C., Ali, L., Williams, G., Beattie, G.: “Waterflood in Vuggy Layer in a Middle East Reservoir-Displacement Physics Understood”, SPE 78530, Abu Dhabi International Petroleum Exhibition and Conference, 13-16 Oct. 2002.        Olivier, P., Cantegrel, L., Laveissière, J., Guillonneau, N.: “Multiphase Flow Behaviour in Vugular Carbonates Using X-Ray”, SCA 2004-13, Society of Core Analysts Symposium, Abu Dhabi, 5-9 Oct. 2004.        
One or more laws K(Φ) are used to deduce from a porosity map a permeability map used for simulation of the tracer experiment. These laws K(Φ) are then manually adjusted until good agreement with the experiment is obtained. The advantage of this approach is its simplicity. On the other hand, a major drawback is that there is a very large number of solutions to this problem. Manual calibration only gives access to a single solution.
Identification of a 3D Map Based on a “Mathematical” Inversion
This technique also uses tracer tests. According to this method, it is possible to monitor, by tomography for example, the displacement of a front at various times. From this information, the permeability map is the solution to a non-linear problem with known boundary conditions. This method is described in:                Zhan, L., Yortsos, Y. C.: “A Direct Method for the Identification of the Permeability Field of an Anisotropic Porous Medium”, SPE 62976, Annual Technical Conference and Exhibition, Dallas, 1-4 Oct. 2000.        
Insofar as the boundary conditions (permeability or pressure profile at the boundaries) and the porosity map are known, this technique leads to a single solution that is valid only when the permeability contrasts are low. Implementation of this technique therefore remains limited in practice because the boundary conditions are not always known. This method does not apply to very heterogeneous media.
1D Profile Based on a Viscous Displacement
Using a viscous displacement to obtain information on the 1D permeability profile was proposed by Fincham and Gouth:                Fincham, A., Gouth, F.: “Improvements of Coreflood Design and Interpretation Using a New Software”, SCA 2000, Society of Core Analysts Symposium, Abu Dhabi, 9-12 Oct. 2000.        
The authors interpret the differential pressure signal of a viscous oil injection at a high flow rate in an initially brine-saturated clump in order to determine the 1D oil permeability profile at Swi. This technique enables better characterization of the “local” heterogeneity of the sample and thus to fine tune the interpretation of the experiments intended to determine the relative permeability curves. However, this approach does not obtain the absolute permeability values, whether in 1D or in 3D.